SOLUTION In this example, we use = BA cos o to solve for the strength of a magnetic field. A plane surface with area 2.6 cm? is placed in a uniform magnetic field that is oriented at an angle of 30° to the surface. (a) What is the angle o? (b) If the magnetic flux through this area is 0.78 mWb , what is the magnitude of the magnetic SET UP AND SOLVE Part (a): (Figure 1) shows our sketch. As defined earlier, ø is the angle between the direction of B and a line normal to the surface, so o = 60° (not 30 °). Part (b): Because B and o are the same at all points on the surface, we can use PB = BAcos o. We solve for B, remembering to convert the area to square meters: field? B= 7.8x10-4 Wb = 6.0 T A cos o (2.6x10-4 m²)(cos 60°) Figure REFLECT The flux through the surface depends on its angle relative to B. Knowing this angle and the flux per unit area, we can find the magnitude of the magnetic field. < 1 of 1 Part A - Practice Problem: A For the same B and A, find the angle o at which the flux would have one third the value given above (i.e., the angle o at which Фв — 2.6 х 10 4 Wb). 30 Express your answer in degrees. B ?

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SOLUTION
In this example, we use = BA cos o to solve for the
strength of a magnetic field. A plane surface with area
2.6 cm? is placed in a uniform magnetic field that is
oriented at an angle of 30° to the surface. (a) What is
the angle o? (b) If the magnetic flux through this area is
0.78 mWb , what is the magnitude of the magnetic
field?
SET UP AND SOLVE Part (a): (Figure 1) shows our sketch. As defined earlier, ø is the angle between the direction of B and a line normal to
the surface, so 0= 60° (not 30 °).
Part (b): Because B and o are the same at all points on the surface, we can use dp = BA cos o. We solve for B, remembering to convert
the area to square meters:
7.8x10-4 Wb
(2.6x104 m?)(cos 60°)
B =
= 6.0 T
A cos o
REFLECT The flux through the surface depends on its angle relative to B. Knowing this angle and the flux per unit area, we can find the
magnitude of the magnetic field.
Figure
< 1 of 1
Part A - Practice Problem:
A
For the same B and A, find the angle o at which the flux would have one third the value given above (i.e., the angle ø at which
Фв — 2.6 х 10 4 Wb).
30°
Express your answer in degrees.
Hνα ΑΣφ
?
圖
Transcribed Image Text:SOLUTION In this example, we use = BA cos o to solve for the strength of a magnetic field. A plane surface with area 2.6 cm? is placed in a uniform magnetic field that is oriented at an angle of 30° to the surface. (a) What is the angle o? (b) If the magnetic flux through this area is 0.78 mWb , what is the magnitude of the magnetic field? SET UP AND SOLVE Part (a): (Figure 1) shows our sketch. As defined earlier, ø is the angle between the direction of B and a line normal to the surface, so 0= 60° (not 30 °). Part (b): Because B and o are the same at all points on the surface, we can use dp = BA cos o. We solve for B, remembering to convert the area to square meters: 7.8x10-4 Wb (2.6x104 m?)(cos 60°) B = = 6.0 T A cos o REFLECT The flux through the surface depends on its angle relative to B. Knowing this angle and the flux per unit area, we can find the magnitude of the magnetic field. Figure < 1 of 1 Part A - Practice Problem: A For the same B and A, find the angle o at which the flux would have one third the value given above (i.e., the angle ø at which Фв — 2.6 х 10 4 Wb). 30° Express your answer in degrees. Hνα ΑΣφ ? 圖
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